Geodesic
A scoop from groups: equational foundations for loops
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 2, pp. 279-290 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Groups are usually axiomatized as algebras with an associative binary operation, a two-sided neutral element, and with two-sided inverses. We show in this note that the same simplicity of axioms can be achieved for some of the most important varieties of loops. In particular, we investigate loops of Bol-Moufang type in the underlying variety of magmas with two-sided inverses, and obtain ``group-like'' equational bases for Moufang, Bol and C-loops. We also discuss the case when the inverses are only one-sided and/or the neutral element is only one-sided.
Groups are usually axiomatized as algebras with an associative binary operation, a two-sided neutral element, and with two-sided inverses. We show in this note that the same simplicity of axioms can be achieved for some of the most important varieties of loops. In particular, we investigate loops of Bol-Moufang type in the underlying variety of magmas with two-sided inverses, and obtain ``group-like'' equational bases for Moufang, Bol and C-loops. We also discuss the case when the inverses are only one-sided and/or the neutral element is only one-sided.
Classification : 03C05, 20A05, 20N05
Keywords: inverse property loop; Bol loop; Moufang loop; C-loop; equational basis; magma with inverses 
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     author = {Phillips, J. D. and Vojt\v{e}chovsk\'y, Petr},
     title = {A scoop from groups: equational foundations for loops},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {279--290},
     year = {2008},
     volume = {49},
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     zbl = {1192.20058},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_2008_49_2_a9/}
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Phillips, J. D.; Vojtěchovský, Petr. A scoop from groups: equational foundations for loops. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 2, pp. 279-290. http://geodesic.mathdoc.fr/item/CMUC_2008_49_2_a9/